The demands made on internal combustion engines, particularly in motor vehicles, are increasing as a result of strict statutory regulations relating to the pollutant emissions and because of customer demands with regard to reliability, the efficient use of operating resources, particularly of fuel, and low maintenance requirements. Such requirements can only be met properly if malfunctions of the vehicle components are detected and recorded reliably and accurately so that malfunctions can be compensated for or repairs of the faulty vehicle components be initiated in each case. To this end, the vehicle components, particularly all the vehicle components specific to exhaust gas, such as for example a catalytic converter unit, a lambda probe and the entire fuel system are monitored. Because of the monitoring measures, it should be possible to ensure low-emission operation and it should be possible to maintain driving safety. This also includes the fact that on the occurrence of errors, an emergency mode of the internal combustion engine can be ensured and consequential damage thus be avoided. The driver of the motor vehicle is informed about the malfunction, if required, so that said driver can initiate a check and/or repair work in a workshop. The monitoring device of the internal combustion engine stores information about the errors which have occurred, such as for example the type of error, the location of the error and the operating conditions under which the malfunction occurred. This information can be evaluated in a workshop and thus supports the repair work.